An aluminum space frame accounts for nearly 25% of the total installation cost of a parabolic trough concentrating solar power (CSP) system, and, therefore, reduction in space frame costs can result in significant savings for a solar project. A reduction of space frame cost can be recognized either in reduction of material (e.g., lighter frames), reduction in manufacturing costs or reduction in installation cost. Because of the size of many large solar thermal installations, the space frames are often thought of as a commodity, and reduction in materials becomes the dominant factor. This does not imply that all components of the frame reduce in size, but rather that there is a net reduction in material used. Reduction in material can be thought of in terms of a net reduction in mass or weight of construction materials or a net reduction in volume of materials required (in cubic space units, such as in3). For a given material the net volume can be equated to a net mass by the following ratio:massn=rn*Vn where r is density and V is volume of material. If the frame is fabricated from more than one material type, the cost reduction can be determined by the equation:costtotal=Σn=1nVolumen*rn*specific costn.
Additionally, increasing the aperture area of a parabolic trough concentrator can decrease overall system costs, but when traditional space frames are scaled to accept large aperture mirrors (e.g., apertures greater than 5.7 meters or 6 meters), the space frame depth must increase to maintain torsional stiffness. But as the space frame increases in depth, the struts become longer making them more susceptible to buckling mode failure.
Critical buckling load is typically defined using Euler buckling, which is a theoretical maximum load that an initially straight column can support without buckling and is given by the equation:
            F      e        =                            pi          2                *        E        *        A                              (                      L            k                    )                2              ,or expressed as a stress:
            s      b        =                  F        e            A                  s      b        =                            pi          2                *        E                              (                      L            k                    )                2            where Fe is the critical bucking load, E is Young's modulus (a material specific property), A is the cross sectional area of the column, L is the unbraced length of the member, and k is the radius of gyration, which is given by:
  k  =            I      A      where I is the area moment of inertia and A is the cross sectional area. In the equation above, both the L and k terms are geometric variables that directly affect the material volume required for a space frame.
By way of example, patent documents describing various space frame designs include, for example, U.S. Pat. Pub. Nos. US 2014/0144428, US 2014/0182580, US 2012/0217209, US 2010/0043776, US 2010/0258702, US 2010/0058703, US 2011/0157733, US 2008/0127595, US 2010/0206303, US 2009/0277440 and US 2008/0308094; U.S. Pat. Nos. 8,615,960, 8,071,930 and 7,950,386; and International Patent App. No. PCT/US2009/04852, each of which is hereby incorporated by reference to the extent not inconsistent herewith.